Meta-Elements

Bohuslav Brauner had approached the rare-earth crisis from a fradifional chemical poinf of view. Bofh the search for higher valencies and complicated atomic weight determinations had been central to his research during the last quarter of fhe nineteenfh century, but neither of fhese methodologies allowed to prove the validity of the homologous accommodation. Brauner s adherence to the Mendeleev method had led him to a 

FIGURE 10 Sir William Crookes (1832-1919). Photo and permission from Edgar Fahs Smith Collection. 

Crookes radiant matter spectroscopic research on the rare earths seemed to point towards the complexity of the elements. It thus provided an excellent empirical basis for his influential lecture On the nature and the probable, or at least possible, origin of the so called elements which 

FIGURE n Crookes mighty pendulum of 1886. Reproduced from Crookes (18861). 

Neither Crookes mighty pendulum (Crookes, 18861) nor his vis generatrix (Crookes, 1888a, 1898) had offered an alternative accommodation for 

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Brauner was completely imaware of the existence of Crookes 1886-1888 lectures. This also explains why Braimer never mentioned the terms metaelements and elemental groups in his 1902 paper. Indeed, the asteroid hypothesis of Brauner could be approved on the basis of Crookes concept of meta-elements, but Braimer himself did never take this step. 

The process meta model introduces the language (or meta schema) for process model definitions. The meta model is based on djmamic task nets. It provides meta elements for structural (tasks, control and data flows etc.) and for behavioral aspects (e.g. state machines for tasks) of these task nets. 

A given chemical element may actually be a mixture of meta-elements with almost identical chemical behavior, but the observed atomic weight is a weighted average of the A values of the meta-elements. 

I. Historical Introduction A. From Meta-Elements to Isotopes... 

Solar systems, or direct diabolic intervention, the writer feels that the exothermic argument is so strong that he, hesitantly, must look for other explanations such as collective hypnosis. Anyhow, for Crookes living 100 years ago, there was still enough of a connection with pre-scientific ideas that he suspected a maturation of the meta-elements in minerals. By the way, this is one of the rare cases of older history being optimistic and newer ideas pessimistic with exception of nuclear physics directed by human beings, the only transmutation of elements on Earth is the irreversible and uninfluenced natural radioactivity of which the chains mranium 238 to lead 206, thorium 232 to lead 208, and the rare isotope potassium 40 to argon 40 (1 percent of the atmosphere) and calcium 40 have a perceptible influence on the heat balance of the crust. 

The meta-elements of Crookes anticipated the idea of isotopes. The most readily available sources of separated stable isotopes are lead 206 from uranium minerals and lead 208 from thorium minerals, and it is interesting enough that before 1910 several successful chemical separations of radioactive isotopes of the same element were reported, involving both thorium 230 (ionium) and lead 210 (radium D). In otir opinion, this can only be due to kinetically metastable chemical nonequivalency in the mixture, for instance, due to colloidal or oligomeric complexes. The valuable conclusion of this story is that the chemical similarity of trivalent rare earths is so striking that doubts have been expressed whether they deserved more than one place in the Periodic Table, a situation isotopes later had to accept. Such a doubt has never been expressed for any other elements, not even for a pair of elements like vanadium and chromium, which were confused at the time of their discovery (7). Nevertheless, studies based on the possibility of metaelements continued rather late for instance, Debierne attempted to separate neo-radium from conventional radium 226 and to perform nuclear reactions on charcoal cooled with liquid helium (77). 

In comparison with absorption spectra, the cathodoluminescence due to impact of rapid electrons is a much less reliable technique for evaluating the concentration of a given luminophore [this difficulty already occurs to a certain extent for photoluminescence (Reisfeld and Jorgensen 1977, 1987)] and it must be admitted today that the different emitters found by Crookes in solids containing R cannot be ascribed to meta-elements [cf. the sharp criticisms by Urbain (1925)]. On the other hand, the ideas of Crookes fit remarkably well the concept of isotopes and their step-wise formation under astrophysically extreme conditions. 

A variable can be used to evaluate system behavior, values are the possible values of a state variable of a hybrid dynamical system. An attribute is of a different nature. Its aim is to represent one of the properties of a meta element. Its values can be generally represented by an object, the chosen format is JSON. 

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